Nyquist-Shannon Sampling Theorem
The Sampling Theorem is the basis for digitizing audio. This sampling theory has been described as “one of the most important mathematical techniques used in communication engineering and information theory“ Zayed, Almed. Advances in Shannon’s Sampling Theory. CRC Press, 1993. pp. 1 History In 1928, Harry Nyquist, a scientis for Bell Labs, first referenced this theorem in his paper, “Certain Topics in Telegraph Transmission Theory.” It was later proved in 1949 by Claude Shannon, a mathematical engineer, in his article “Communication in the Presence of Noise.” Although others have made contributions, it is Nyquist and Shannon for whom the theorem is named. Nyquist's name has been attached to the theorem as early as 1959 in a book by his former employers, Bell Labs. Members of the Technical Staff of Bell Telephone Lababoratories (1959). Transmission Systems for Communications. AT&T. pp. 26–4 (Vol.2). Likewise, Shannon's name has been associated with the theorem in works as early as 1954. Truman S. Gray, Applied Electronics: A First Course in Electronics, Electron Tubes, and Associated Circuits, 1954. The Theorem The Nyquist-Shannon Sampling Theorem says that a signal can be reconstructed when the sampling rate is more than twice the maximum frequency of the signal being sampled. This rule tells us that to reproduce sounds as high as human hearing 20,000 hertz we must take at least 40,001 samples per second. The standard sampling rate for digital music in the music industry is 44.1kHz and each sample is assigned 16 bits. Some theorem definitions describe this process as making a perfect recreation of the signal. Luo, Fanglin., Ye, Hong., Rashid, M.H., Digital power electronics and applications. Academic Press, 2005. pp. 94 Aksoy, Pelin., DeNardis, Laura., Information Technology in Theory. Cengage Learning, 2007. pp. 132 Sampling, the process of converting a signal into a numeric sequence is also called analog–to–digital conversion. Quantization is another process of the conversion, which is the accurate measurement of each sample. Analog to digital converters and digital to analog converters encode and decode these signals to record our voices, display pictures on screen, or to play audio clips through speakers. Since we can digitize media we can handle, recreate, alter, produce, and store text, images, and sounds. The theorem even though it can be seen as simple has changed the way our modern digital world works. We can uniformly use media to our advantage in multiple numbers of ways. The limitations we have can be addressed through filters and adjusting our sample rates or frequencies. The theorem helps us to understand what is possible and what can be done to fix any errors that might occur. Storing audio has always had its limits, even digital audio can fill a hard drive quickly if you’re not careful with monitoring your space. Audio compression formats have become more effective every year. Tiny devices can store thousands of MP3s by having compressed audio, that is not as high quality as everything else but its worth the lower quality for the massive amount of storage. The theorem also makes this possible by allowing us to adjust accordingly for how much space and music we have. Jerry D. Gibson states the sampling theorem is the fundamental principle of digital communications.Gibson, Jerry D., Mobile Communications Handbook on CD-ROM. CRC Press, 1999. Section 2.8 It can take you from the real analog world to the recreated digital world and back again. It governs all media and must be respected because it is the beginning and the end to our modern digital world. References